Fingías comes from the verb fingir, meaning "to pretend" or "to feign". It's a less common verb than pretender (to intend/try) and carries a stronger sense of deception.
In the song, the narrator sings, "Yo sin saber que me fingías" (I, without knowing that you were pretending to me). This word is key to understanding the heartbreak and betrayal felt by the singer, as it reveals that the love he thought was real was, in fact, a lie.